They may be using Preview which is in an inferior reader. Tell them to use Reader or Acrobat.
Sorry, forgot to specify, client's Mac runs current OS and current Adobe Reader, which they're using.
For what it's worth, I discovered that the traits to my PDF that would make it behave like a slideshow, the way I wanted it, was resident in Adobe Reader, in Preferences > Full Screen. There are interval controls and anything.
The implication is, any multi-page PDF can be shown, even projected, as a slide show.
The transitions, however, were imparted into it via InDesign. So go figure.
Auto advancing slides in Acrobat/Reader are an application preference: Full Screen > Advance Every X seconds. There is no way to set this option for other users.